4awg is thicker. it has more strands. this allows for more current to flow. depending on the length of wire you are running, your amp will not perform to its potential if you use too small of a wire.
if the wire is too small, it'll build up too much heat. this will cause a possible fire, as well as causing the amp to be starved for current, which will send the amp into clipping, which will burn up your speakers.